The Word Symmetry in Physics Is Consistent, Right?

The word symmetry is that it has to do with the equations of a motion of the universe, right? Like if you apply, like a mirror transformation, or some kind of transformation to equations, then it should stay the same. Or even if i moved to earth a few light ears to the right, it should still be the same, right? Ye, if you knew the whole universe rit a few light years to the rightbut nobody could do an experiment to determine that's the case,. Because no place in space is different, right? The rules should be the same everywhere, right? So when you hear the word symmetry and physics really me in your head, you should be like